Ars Mathematica

Bousquet, Boucheron, and Lugosi have authored a short introduction to statistical learning theory.

Found here.

Finally, something we’re not number one at. In empirical research at its finest, this paper has investigated ratings at RateMyProfessors.com, and determined that mathematicians are not number one, either in easiness, or in hotness. (We’re also not 36th out of 36 in either — this honor is reserved for chemists in both categories.)

Here’s an interesting little tidbit I spotted today. Polynesians once traveled throughout the South Pacific by canoe. Apparently, one way they navigated was by stick charts, which were bits of wood woven together to represent both the locations of islands and the direction of ocean waves. The charts themselves look like abstract sculptures rather than anything we would recognize today as maps.

More, including pictures, here.

As I’m sure everyone has heard by now, the site Career Cast announced the top professions. Number 1 is mathematician, number 2 is actuary, and number 3 is statistician. The top of the list features other taxing careers such as accountant and historian. It sounds like the metric was the reciprocal of physical exertion.

The language of schemes relies on a dramatic extension of the notion of points. David Mumford’s Red Book on Varieties and Schemes is full of drawings that try to communicate these exotic new sorts of points. Lieven Le Bruyn explains.

Aimless websurfing has taught me that mathematics is apodictic. Now you know.

I was musing on the fact that I have never heard a psychologically plausible account of the appeal of pure mathematics. (I say “pure” mathematics because I suspect pure and applied mathematics have different sources of appeal). By “psychologically plausible”, I mean one grounded on the psychology of individual mathematicians. Lots of mathematicians have written explanations of the appeal, but most of these are either of the form “Because mathematics is awesome.”, or “Because I’m awesome” While mathematics is awesome, and while I’m willing to grant the premise that I’m awesome pretty much any time it comes up, these explanations lack the kind of specificity I have in mind. One common explanation, for example, is that math is like music, which relies on the presupposition that music is intrinsically valuable, and that math has value by analogy. But why do we like music? What in the psychology of mathematicians makes math seem like music to them? These are harder questions than the original one. Another explanation is that math is challenging, which is a subspecies of the “I’m awesome”. But in what way is mathematics challenging to mathematicians? Mathematicians, as a group, do not strive to be Nietzschean superman endlessly trying to overcome their limitations, so why this particular challenge, rather than the Nathan’s hot dog eating contest, or climbing Everest?

There are psychological explanations floating around as stereotypes, most of which are immensely unflattering, but are least examples of the kind of explanation I have in mind. One example is that mathematicians are like the Rain Man in that they just like repetitive tasks like counting or adding. Another example is that mathematicians can’t handle the real world, and so retreat to the safety of the world of numbers. These are both wrong and insulting, but they are at least grounded in the psychology of individual mathematicians. If anyone has a non-wrong explanation, I’d be curious to hear it.

Slashdot has a thread discussing physics books recommendations for a math Ph.D. student who would like more physical intution into partial differential equations. There are some good suggestions, and many comments that come dangerously close to “You’re a math Ph.D. student and you don’t know what a PDE is?”